Wikipedia:Reference desk/Archives/Mathematics/2016 February 13

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February 13

How do I inflate an older amount of money (from past years) into a modern-day amount?

Oftentimes, I will see statements such as this: "$500 in 1962, which is the equivalent of $10,000 in 2016" (using hypothetical numbers). These statements often appear right here in Wikipedia. What is the mathematical formula to make such conversions? I tried some online calculators, but they typically ask me to input interest rates or such. I had assumed there was a standard method of converting dollar values from X years ago into today's currency values. Thanks. Joseph A. Spadaro (talk) 03:34, 13 February 2016 (UTC)

In modern times these calculations are normally based on the consumer price index for the applicable country: it's not like an interest calculation where you assume a specific rate of growth each year, but just a table lookup of actual inflation and then a simple proportionality. (If you're projecting monetary values into the future, then you might do something like an interest calculation because you'll have to assume what the rate of inflation will be.) But if you're talking about ancient or even pre-industrial times, the comparisons get more dicey as the things people spend money on have changed so much. (Should the price index include the price of a telephone, for example? The price of having your horse shod?) --76.69.45.64 (talk) 03:50, 13 February 2016 (UTC)

In ancient times, there are two ways that can reasonably be used to convert money. The first, appropriate for large amounts of money, would be to use the current price of gold or silver applicable to the quantity. The second, for smaller amounts of money, is sometimes applicable in biblical scholarship, which that sometimes a particular amount, such as the denarius, is referred to as the usual daily wage. In that case, it can be converted to the modern daily minimum wage (approximately $60 USD in the US). Robert McClenon (talk) 03:54, 13 February 2016 (UTC)

You would just multiple by the inflation rates for each intervening year. For example, if something with a stable value was worth $100, then 3 years passed, with 3%, 5%, and -1% inflation rates, then the value after those 3 years should be 100×1.05×1.03×0.99 = $107.07. This process would get rather tedious and error prone for large numbers of years, so a program would normally be used to do the calcs.

However, as mentioned previously, the longer the elapsed time, the less accurate such calcs are. In your 1962 to 2016 example, lets say we wanted to compare the price of the average car then to the average car now, adjusted for inflation. We could do the math, but the average car then would have been a very different thing, with no airbags or safety belts, probably a minimal radio, if any, likely a manual clutch, maybe no power steering or brakes, but with rear drum brakes, bias-ply tires, perhaps 12 mpg, etc. (on the plus side, at least the 1962 car would have likely had a full-sized spare). So, you would be comparing apples and oranges. StuRat (talk)

Yeah, basically there's a lot of arbitrariness in any particular calculation of inflation. How do you tell how much of the change in a price is related to a change in the value of money (inflation), versus a change in the utility of the good or service being purchased? Utility is inherently subjective anyway; you can't reliably compare it intersubjectively, except by observing what people are willing to trade on a willing buyer–willing seller basis. And you can't set up such a trade across multiple years, or maybe you can, but then you have another factor to consider, which is the time value.

Still, we can get an idea of the inflation rate by considering a "basket", the way the CPI does, at least assuming that the goods in the basket are actually available at their nominal prices (which they won't be in a price-control regime, but usually are otherwise). But different baskets will give different answers. Maybe not too different in any one year, but the errors will add up.

So basically I would take with a big grain of salt any pronouncements about what a given amount of money was worth over a time range more than, I don't know, a century or so. You can get a rough idea. But to get a really meaningful answer, you have to ask a different question, which is something like "what would my life be like on an income of such-and-such?". That's not necessarily going to lend itself to an answer that can be captured by a single number. --Trovatore (talk) 06:49, 13 February 2016 (UTC)

Thanks. But the answers are getting much too complicated for what I had thought was an easy calculation. So, let me re-phrase. (1) Is there an online calculator where I can enter the two years in question and the amount, and get as a result the new amount? Example: How much is $500 from 1959 worth in today's money (2016)? That sort of thing? That's a very basic question. But I certainly don't know the CPI for all of those 50+ intervening years. I assume the calculator "knows" this? (2) How are these numbers created in Wikipedia articles? I often see articles that say "his salary in 1959 was $500, which is valued at $10,000 in 2016 dollars" (or some such). Thanks. Joseph A. Spadaro (talk) 21:49, 13 February 2016 (UTC)

In Wikipedia, Template:Inflation is used and it has surprisingly good documentation. For your example {{Inflation|US|500|1959|2016}} gives the answer $4116. Thincat (talk) 23:01, 13 February 2016 (UTC)

Thanks. Yes, that is exactly what I was looking for. Joseph A. Spadaro (talk) 02:17, 14 February 2016 (UTC)

I will note that nearly all of the above discussions are really only applicable to conversion between modern prices and current prices in a given country's money, where there is a Consumer Price Index relying on some sort of reasonably well-defined basket, which is periodically adjusted, within the country, or perhaps between two industrial countries. It is hard enough to provide a reasonable comparison between an industrial country and an industrializing country, both in 2016, where what people live with are different in the different countries. Trying to use a basket or comparison gets really messy trying to view prices in the past in a less industrial country with those of the modern US, UK, or EU. As I noted above, the best ways to compare prices in ancient times with value in modern terms are, for large amounts of ancient money, use the modern price of gold or silver, and, for lesser amounts of money, if an amount is defined in a daily wage, compare to the modern minimum daily wage. In the Bible, Jesus's disciples complain that it would take two hundred times the daily wage to feed a multitude. That is $12,000 US. (So Jesus prefers to work a miracle, or the story is mythical; take your pick.) Robert McClenon (talk) 23:10, 13 February 2016 (UTC)

I am talking about modern days, not archaic or Biblical times. Thanks. Joseph A. Spadaro (talk) 02:17, 14 February 2016 (UTC)

Thanks, all. Joseph A. Spadaro (talk) 21:28, 18 February 2016 (UTC)